The Saudi Ministry of Foreign Affairs issued a statement condemning "the sabotage and violence carried out by some armed groups" on the embassy in Sudan as well its ambassador and embassy staff.
It called for "confronting these groups that are trying to undermine [the] security and stability [of] Sudan and its people".
Bahrain's Foreign Ministry said its embassy and the ambassador's residence were attacked and vandalised, leaving the building damaged.
The ministry emphasised "the need to stop acts of violence and vandalism in Sudan and to provide the full protection for the headquarters of diplomatic missions and civilian facilities".
All parties to the conflict must "give priority to national interests and must respond seriously to the Saudi-US initiative" to stop the war, it said.
The attacks were condemned by the Arab League and the Arab Parliament.
Fighting between Sudan's military and the rival Rapid Support Forces paramilitary has continued since mid-April despite efforts by Saudi Arabia, the US and other countries to broker a ceasefire.
A humanitarian truce brokered by Riyadh and Washington was suspended only days after coming into effect on May 22.
The fighting has inflicted a heavy toll on civilians, particularly children.
More than 860 civilians, including at least 190 children, have been killed and thousands of others wounded since April 15, according to Sudan's Doctors' Syndicate which tracks civilian casualties. The actual death toll is likely to be much higher.
The conflict has forced more than 1.9 million people to flee their homes, including about 477,000 who crossed into neighbouring countries, according to the UN's migration agency.
Others remain trapped in their homes, unable to escape as food and water supplies dwindle.
The clashes have also disrupted the work of humanitarian groups.